Controlled remote state preparation and controlled probabilistic quantum key distribution based on AKLT ground state

• Main Authors: Lin-LinLiu, 劉麟麟
• Other Authors: Tzone-Lih Hwang
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/61345707463722337726

博士 === 國立成功大學 === 資訊工程學系 === 103 === It is believed that the security of classical cryptography (e.g., RSA, ElGamal), being based on mathematical problems, will be broken by the parallel computing of quantum computers and quantum computing. Researchers in the field of information security hope to overcome this using quantum cryptography, which is based on quantum phenomena (mechanics). Therefore, many quantum protocols regarding cryptography topics have been developed and proposed in this decade. Quantum protocols always need quantum states as a resource to build their quantum channels. Different states have different properties, making protocols very masterful. Quantum entanglement, i.e., the correlation between particles in a multi-particle quantum state, is one of the central principles of quantum physics and an important property of quantum mechanics. In recent years, many quantum protocols have been realized using well-known entangled states such as the EPR pair, GHZ state, GHZ-like state, and W state. However, to the best of our knowledge, few schemes employ the AKLT ground state, which is also an entangled state. The AKLT is the gapped ground state of a spin-1 chain with a two-body nearest-neighbor interaction. The gapped ground state has a minimized energy gap between the ground state and the first excited state. The property of the small energy gap allows the ground state to have an easy maintenance. This motivates us to develop controlled protocols using the AKLT ground state. All entangled states are generated based on specific physical mechanisms and with different measurement properties and are widely used in quantum cryptography. The properties of these entangled states, including the AKLT state, will be briefly described in this thesis, and we will mention the AKLT ground state for its special property. The property of the AKLT state not only allows easy control by the controller but also increases the randomness in the quantum protocol. Therefore, we have more incentives to structure our controlled protocols using the AKLT ground state as a quantum resource. This thesis investigates the properties of AKLT states and proposes four controlled protocols. First, two controlled-remote-state-preparation (CRSP) protocols using AKLT states are proposed. Then, two controlled-probabilistic-quantum-key-distribution (CPQKD) protocols are developed using AKLT states.